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Advanced Algebra II Advanced Algebra II Notes 10.2 Radian Measure and Arc Length

Advanced Algebra II Advanced Algebra II Notes 10.2 Radian Measure and Arc Length.

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Advanced Algebra II Advanced Algebra II Notes 10.2 Radian Measure and Arc Length

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  1. Advanced Algebra IIAdvanced Algebra II Notes 10.2 Radian Measure and Arc Length

  2. Radian: An angle measure in which one full rotation is 2 radians. One radian is the measure of an arc, or the measure of the central angle that intercepts that arc, such that the arc’s length is the same as the circle’s radius. Converting degrees and radians: angle in degrees = angle in radians 360° 2 Π

  3. Convert degrees to radians or radians to degrees: a) b) n radians c) 225° d) n°

  4. Length of an Arc and Area of a Sector: Given an angle in RADIANS: Arc length Area of a sector Circle O has diameter 10 m. The measure of central angle BOC is 1.4 radians. What is the length of its intercepted arc BC? What is the area of the shaded sector?

  5. The Cosmo Clock 21 Ferris wheel at the Cosmo World amusement park in Yokohama, Japan has a 100 m diameter. This giant Ferris wheel makes one complete rotation every 15 minutes. The wheel reaches a maximum height of 112.5 m from the ground. a) Find the speed of a person on this Ferris wheel as it is turning. b) Find the angular speed of this person. is the angular displacement (in radians) s is the arc length or distance (in linear units) is the angular velocity (radians per time) v is the velocity or speed (linear units per time)

  6. Assignment: page 578: 1 – 8, 10, 12

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